From work carried out at the Goodyear-Zeppelin Corporation (now Goodyear Aircraft Corporation) the authors have derived general solutions for certain ring problems. The paper briefly discusses the difficulties in usual methods of studying structures with large numbers of redundancies and discusses simplifications which can be made in these methods when the structures are symmetrical. The remainder of the paper discusses the application of trigonometric series to stiffened-ring problems. General solutions are derived by using differential equations of equilibrium for the case of circular rings with continuous radial support, and by using difference equations of equilibrium for the case of polygonal rings with spokes and loads at the corners. Shear and axial strains in the ring and the difference in length of inner and outer fibers of the ring are considered. Finally the paper shows how complete solutions can be obtained by similar methods for the case of spoked and trussed rings under loads at the joints.